## Library Engine: Linear algebra

Linear algebra engine.

The linear algebra engine provides support for calculation with vectors and matrices.

 inv(matrix)Matrix inverse. pinv(matrix)Moore–Penrose pseudoinverse. min(args)Minimum of arguments. max(args)Maximum of arguments. mean(args)Average of elements. sum(args)Sum of elements. reciprocalSum(args)Reciprocal sum of elements. product(args)Product of elements. average(args)Average of elements. eye(width, height, fill)Unit matrix. cross(a, b)Cross product of two 3D vectors. dot(a, b)Dot product of two vectors. proj(a, b)Orthogonal projection. zeros(h, w)Create a matrix filled with zeros. ones(h, w)Create a matrix filled with ones. diag(what, offset)Diagonal matrix. diags(mtx, offset)Selects diagonals of a matrix. gauss(matrix, argument)Gaussian elimination. det(matrix)Determinant of a matrix. size(arg)Return the matrix size of the argument. rank(mat)Rank of a matrix. rref(mat)Reduced row echelon form of a matrix. rankDecompose(mat)Decompose a matrix to linearly independent rows and columns. givens(p, q)Calculates the Givens rotation matrix. jacobi(p, q, r)Jacobi conjugation. householder(v)Householder rotation. eig(mat, details)Gives generalised eigenvalues and vectors of A. svd(mat, details, narrow)SVD: singular value decomposition. schur(mat, details)Schur decomposes matrix A to QR, where Q is unitary, and R is triangular. hess(mat, details)Implements Hessian decomposition. funcAtMatrix(func, mat)Evaluates a square matrix at a function.